If you start with 2 and count by 3s until you reach 449, you will get the sequence: 2, 5, 8, 11, …, 449. If 449 is the Nth numbe
1 answer:
Answer:
150
Step-by-step explanation:
The terms in the sequence form an arithmetic sequence with n th term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 2 and d = 3 , thus
2 + 3(n - 1) = 449
2 + 3n - 3 = 449
3n - 1 = 449 ( add 1 to both sides )
3n = 450 ( divide both sides by 3 )
n = 150
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Answer:
0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the approximate probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true?
This is 1 subtracted by the pvalue of Z when X = 3.1. So
By the Central Limit Theorem
has a pvalue of 1.
1 - 1 = 0
0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.